In this article, we build an approximate solution to an Inverse Problem that consist in ﬁnding a function whose Caputo fractional derivative is given. We decompose and project the data in appropriate wavelet subspaces and, by a Galerkin scheme, we calculate the coefﬁcients of the unknown function in the chosen wavelet basis. Based on properties of the operator and of the basis, the scheme is simple, efﬁcient and the errors introduced by the approximation can be handled and controlled. We illustrate the results with an example.
Digital Object Identifier (DOI)
A. Fabio, Marcela and I. Troparevsky, Marıa
"An Inverse Problem for the Caputo Fractional Derivative by Means of the Wavelet Transform,"
Progress in Fractional Differentiation & Applications: Vol. 4
, Article 3.
Available at: https://dc.naturalspublishing.com/pfda/vol4/iss1/3